Answer to Quiz 1 Math 618 1. Eric deposits $100 into a savings account at time 0, which pays interest at a nominal rate of i, compounded semiannually. Mike deposits $200 into a different savings account at time 0, which pays simple interest at an annual rate of i. Eric and Mike earn the same amount of interest during the last 6 months of the 8th year. Calculate i. A. 9.06% B. 9.26% C. 9.46% D. 9.66% E. 9.86% Answer: C 2. Jeff deposits $10 into a fund today and $20 fifteen years later. Interest is credited at a nominal discount rate of d compounded quarterly for the first 10 years, and at a nominal interest rate of 6% compounded semiannually thereafter. The accumulated balance in the fund at the end of 30 years is $100. Calculate d A. 4.33% B. 4.43% C. 4.53% D. 4.63% E. 4.73% Answer: C 3. David can receive one of the following two payment streams: • 100 at time 0, 200 at time n, and 300 at time 2n • 600 at time 10 At an annual effective interest rate of i, the present values of the two streams are equal. Given vn = 0.76, determine i. A. 3.5% B. 4.0% C. 4.5% D. 5.0% E. 5.5% Answer: A 4. Bruce and Robbie each open up new bank accounts at time 0. Bruce deposits 100 into his bank account, and Robbie deposits 50 into his. Each account earns the same annual effective interest rate. The amount of interest earned in Bruce’s account during the 11th year is equal to X. The amount of interest earned in Robbie’s account during the 17th year is also equal to X. Calculate X. A. 28.0 B. 31.3 C. 34.6 D. 36.7 E. 38.9 Answer: E 5. Ernie makes deposits of $100 at time 0, and X at time 3. The fund grows at a force of interest δt = t 2 100, t > 0 The amount of interest earned from time 3 to time 6 is also X. Calculate X. A. 385 B. 485 C. 585 D. 685 E. 785 Answer: E 6. At a nominal interest rate of i convertible semi-annually, an investment of 1000 immediately and 1500 at the end of the first year will accumulate to 2600 at the end of the second year. Calculate i. A. 2.75% B. 2.77% C. 2.79% D. 2.81% E. 2.83% Answer: D 7. Calculate the nominal rate of discount convertible monthly that is equivalent to a nominal rate of interest of 18.9% per year convertible monthly. A. 18.0% B. 18.3% C. 18.6% D. 18.9% E. 19.2% Answer: C 8. A bank offers the following choices for certificates of deposit: Term (in years) Nominal Rate Convertible Quarterly 1 4.00% 3 5.00% 5 5.65% The certificates mature at the end of the term. The bank does NOT permit early withdrawals. During the next 6 years the bank will continue to offer certificates of deposit with the same terms and interest rates. An investor initially deposits 10,000 in the bank and withdraws both principal and interest at the end of 6 years. Calculate the maximum annual effective rate of interest the investor can earn over the 6-year period. A. 5.09% B. 5.22% C. 5.35% D. 5.48% E. 5.61% Answer: D 9. The parents of three children, ages 1, 3, and 6, wish to set up a trust fund that will pay X to each child upon attainment of age 18, and Y to each child upon attainment of age 21. They will establish the trust fund with a single investment of Z. Which of the following is the correct equation of value for Z? A. Xv17 + v15 + v12 + Yv20 + v18 + v15 B. 3 bracketleftBig Xv18 + Y 21 bracketrightBig C. 3Xv3 + Y bracketleftBig v20 + v18 + v15 bracketrightBig D. (X + Y )v 20 + v18 + v15 v3 E. X bracketleftBig v17 + v15 + v12 bracketrightBig + Y bracketleftBig v20 + v18 + v15 bracketrightBig Answer: E 10. Bruce deposits $100 into a bank account. His account is credited interest at a nominal rate of 4% convertible semiannually. At the same time, Peter deposits $100 into a separate account. Peter’s account is credited interest at a force of interest of δ. After 7.25 years, the value of both accounts are the same. Calculate δ. A. 0.0388 B. 0.0392 C. 0.0396 D. 0.0404 E. 0.0414 Answer: C 11. A store is running a promotion during which customers have two options for payment. Option one is to pay 90% of the purchase price two months after the date of sale. Option two is to deduct X% off the purchase price and pay cash on the date of sale. A customer wishes to determine X such that he is indifferent between the two options when valuing them using an effective annual interest rate of 8%. Set up an equation that the customer need to solve. A. parenleftbigg X 100 parenrightbiggparenleftbigg 1 + 0.086 parenrightbigg = .90 B. parenleftbigg 1− X100 parenrightbiggparenleftbigg 1 + 0.086 parenrightbigg = .90 C. parenleftbigg X 100 parenrightbigg (1.08)1/6 = .90 D. parenleftbigg X 100 parenrightbiggparenleftbigg1.08 1.06 parenrightbigg = .90 E. parenleftbigg 1− X100 parenrightbigg (1.08)1/6 = .90 Answer: E